To save and restore window state in iTerm2 under macOS Sonoma, follow the below steps.

1. Disable Close windows when quitting an application option from System Preference > Desktop & Dock under macOS Sonoma.

2. In iTerm2 > Settings > General > Start up, choose Window restoration policy: Use System Window Restoration Setting.

3. In iTerm2 > Window > Save Window Arrangement and specify a name.

4. After launching iTerm2 and to open this arrangement in the current window use Window > Restore Window Arrangement and choose the name.

5. To restore the window arrangement as new tab, use Window > Restore Window Arrangement as Tabs.

I moved to iTerm 2 because macOS Terminal is not able to display full range of colours. So the vim theme isn't working.